By Nozer D. Singpurwalla
This preface relates to 3 concerns that we'd wish to carry to the eye of the readers: our ambitions, our meant viewers, and the character of the fabric. we have now in brain a number of pursuits. the 1st is to set up a framework for facing uncertainties in software program engineering, and for utilizing quantitative measures for selection making during this context. the second one is to convey into point of view the big physique of labor having statistical content material that's appropriate to software program engineering, that can now not have seemed within the conventional shops dedicated to it. hooked up with this moment goal is a wish to streamline and manage our personal considering and paintings during this quarter. Our 3rd goal is to supply a platform that allows an interface among laptop scientists and statisticians to deal with a category of difficulties in laptop technological know-how. it seems that such an interface is important to supply the wanted synergism for fixing a few tough difficulties that the topic poses. Our ultimate goal is to function an agent for exciting extra cross-disciplinary learn in laptop technology and facts. To what volume the fabric right here will meet our ambitions can basically be assessed with the passage of time. Our meant viewers is desktop scientists, software program engineers, and reliability analysts, who've a few publicity to chance and statistics. utilized statisticians attracted to reliability difficulties also are a section of our meant audience.
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Additional resources for Statistical Methods in Software Engineering: Reliability and Risk
The likelihood function not being a probability need not obey the laws of probability; that is, the function when summed (or integrated) over all values Xl need not equal one. In fact there is a well-known example in the analysis of software failure data [cf. Forman and Singpurwalla (1977)] wherein the likelihood function integrates to infinity. , for the fixed value X2) to the various values Xl that Xl can possibly take. 6) will then take the form/(xl I Xl> H) ex: / (X2 I Xi> H) / (Xl I H), with / (X2 I Xi> H) the likelihood function, and the other terms the probability densities.
The number of events occurring in disjoint time intervals are independent random variables. This property is known as the independent increments property, and is a defining characteristic of all Poisson process models. An advantage of having such a property is the ease with which statistical inference for Poisson process models can be done; a specification of the likelihood function is straightforward. However, assumption (i) is very strong and often unrealistic. Despite this, Poisson process models have been used to describe software failures [cf.
N (~) . (x - 1) . (x - 2) ···2· denotes the quantity 1. Poisson's Approximation to the Binomial Distribution In many applications involving Bernoulli trials, it can happen that N is large and (l - p) is small, but their product N x (1 - p) is moderate. In the case of software testing, this situation arises when software that is almost bug free is subjected to a large number of inputs, so that (1 - p) is small and N very large so that N x (1 - p) is moderate. When such is the case it is convenient to use an approximation to the binomial distribution, which is due to Poisson.